Question

$ABCD$ is a rectangle in which $AB=2BC$. If $M$ is the mid-point of $BC$ and the diagonal $BD$ meets $AM$ at $O,$ prove that
$△BOM\sim △AOD$

Answer 1

Ref.Image.

AB = 2 BC ... (given)

In $\Delta$ BOM and $\Delta$ AOD

$\angle$ BOM = $\angle$AOD ... (vertically opposite angles)

$\angle$ OBM = $\angle$ ODA .... (ultemate angles)

$\Delta$ BOM $\sim$ $\Delta$ AOD ... [AA test of similarity ]